Magnetism Magnets are used in meter, motors, speakers, CDs, MRIs, cyclotrons and to store computer data. They are used to move heavy objects, propel trains and store antimatter. Changing magnetic fields will produce electricity

Magnets A magnet consists of of a north and south pole which attract each other. No matter how many time a magnet is cut all pieces will have a N and S pole. Unlike an electric charge, magnetic poles do not exist by themselves. Soft metal (iron) is easily magnetized and easily loose that magnetism.

Cont. Hard metals, (cobalt, nickel) are difficult to magnetize, but retain their magnetism Permanent magnets can be created by close proximity to magnetic material. Electromagnets occur due to the presents of an electric current that temporarily polarizes a metal core. Magnetic field surround magnetized material moving from north to south pole. (a vector)

Earth’s Magnetic Field A small magnetic bar (compass) will seek out earth’s magnetic field. S end of the bar points north and the N end points south. The magnetic axis of earth is 11 o tilt to the axis of rotation. (magnetic declination) At the equator a compass needle will be horizontal. Further N or S the needle will additionally tilt towards the earth.(dip angle

Cont. Earth’s magnet field is coursed by an electric current in the rotating liquid part of the earth’s core and earth’s rotation. Jupiter that rotates faster has a stronger magnetic field. Every few million years the earth’s magnetic field reverses. (evident in basalt rock) Some birds use earth’s magnetic field to migrate and anaerobic bacteria have magnetite as part of their internal structure.

Magnetic Fields When a charged particle moves through a magnetic field the field’s force acts on the particle. It is maximum when the movement is perpendicular to the field and zero when moving parallel to the field. Magnetic force ( B ) on a moving charge is directed perpendicular to the magnetic field.

Fields cont. The magnetic force on a charged particle is proportional to the charge q, (C) the velocity of the charge v,(m/s) the magnitude of the field B (tesla T = weber Wb/m 2 ) and the angle of movement to the field. F = qvBsin  at 90 o F max = qvB 1 C moving at 1 m/s in a field of 1 T experiences a force of 1 N In cgs units 1 T = 10 4 G (gauss)

Electric Force on a Current-Carrying Conductor Like a single charge, magnetic force is exerted on a current carrying wire. The force on the wire is the sum of the individual forces on the charged particles. Consider a length of wire = l, with cross- sectional area A, carrying a current I in a magnetic field B. The velocity = v d and n is the number of unit carriers per unit volume.

Cont. Then Fmax = (Qvd B)(nAl) as I = nqvdA then Fmax = BIl * *this equation is only true when current and magnetic field are at right angles to each other. If the wire is at some angle to the field then F = BIlsin  where  is the angle between the field and current. If the current is in the, or opposite the direction of the field the force is zero.

Torque on a Current Loop and Electric Motors If a loop of wire is placed in a magnetic field a torque is exerted on a flowing current in b. B a b I Force on a is zero, Force on b F 1 =F 2 =BIb

Cont. The direction of the force on the left side is out and the direction on the right side is in.(right hand rule) Viewed from the side F1F1 F2F2 B O a /2 Rotate around O clockwise

Cont. Torque = force x distance T = F 1 (a/2) + F 2 (a/2) = BIb(a/2) +BIb(a/2) = BIab As the area of the loop = A = ab then T max = BIA only if field is parallel to loop If the field makes an angle with the loop T = BIAsin 

Torque on a Coil Let N = the number of turns in a coil then T = BIAN sin  Let  = IAN ( magnetic moment of coil) then T =  B sin  where  is the angle between the magnetic moment and the magnetic field.

Electric Motors Motors convert electric energy to kinetic energy of rotation by use of a current carrying coil loop rotating in a magnetic field. Because the angle between loop and field as the loop rotates goes from 90 to 0, when it passes 0 it will reverse unless the current reverses direction. In an AC current this occurs 120 times per second allowing continual rotation.

DC motors In a DC motors current reversal is accomplished mechanically with a split ring contact ( commutators) and brushes. As the brushes cross the gaps in the ring they cause the loop current to change direction. This change in direction of current causes continual rotation.

Right Hand Rule To determine the direction of magnetic force with respect to motion and magnetic field, use the right hand rule. 1) point fingers of right hand in the direction of the velocity 2) curl the fingers in the direction of the magnetic field, moving through the smallest angle 3)The thumb points in the direction of the magnetic force exerted on a positive charge

Charged Particle Motion in a Magnetic Field When the velocity of a charged particle is perpendicular to a uniform magnetic field, it moves in a circular path perpendicular to that field. The magnetic force is always directed to the center of the circular path, thus causing centripetal acceleration. F = qvB = (mv 2 )/r or r = (mv)/(qB) The latter is called the cyclotron equation

Cont. The radius of the path is proportional to the momentum and inversely proportional to the charge If the initial direction of the velocity is not perpendicular to the magnetic field the path followed by the particle is a helix (spiral), along the magnetic field lines.

Magnetic Field Caused by a Conductor If a constant current is passed through a long conductor a circular magnetic field forms around the conductor. Using the RHR, point thumb in the direction of the positive current and curled fingers point in the direction of the magnetic field. The strength of that field is given by B = (  o I)/(2  r) where  o = 4  x T.m/A

Ampere’s Law Consider an irregular shaped path around a magnetic field. The length of the path can be divided into small segments of  l. Multiplying this segment by the magnetic filed parallel to it gives B II  l. Ampere’s Law states that the sum of all the products over a closed path is equal to  0 x I (Current passing through the closed path) Ampere’s circuital law  B II  l =  0 x I

Magnetic Force Between Two Parallel Conductors Two long parallel wires separated by distance d carrying currents I 1 and I 2 will exert a magnetic force upon each other due to the magnetic fields they each create. The magnetic field created by wire 2 is given by B 2 = (  o I 2 )/(2  d) The force on wire 1 due to B 2 is F 1 = B 2 I 1 l = [(  o I 2 )/(2  d)]I 1 l= (  o I 2 I 1 l)/(2  d)

Cont. Parallel conductors carrying currents in the same direction attract each other Parallel conductors carrying currents in opposite directions repel each other.

Magnetic Fields of Current Loops and Solenoids If a current carrying conductor is formed into a loop the magnetic field is enhanced by the fact that opposite positions on the loop reinforce each other ( have the same magnitude). The magnetic field produced is at the center of the loop. The magnitude is given by B = (  o I)/2R where R is the radius of the loop.

Cont. When a coil has N loops each carrying current I, the magnetic field at the center is given by B = N[(  o I)/2R] The formation of this coiled wire carrying a current is called a solenoid, (electromagnet). Only when current flows is it a magnet and its strength increases with an increase in current strength and number of coils per unit length.

Cont. The magnet field lines inside a solenoid are nearly parallel and produce a field stronger that outside the solenoid. The field inside the solenoid has a constant magnitude. Outside the solenoid the field lines move in the opposite direction, are not uniform and form a weaker field. North = direction of I Field magnitude inside B =  o nI n = N/l

Magnetic Domains Considering that an electron ( a charged particle ) moves in a circular orbit, it produces a magnetic field of the order of 20T, at the center of the orbit. Atoms should be large scale magnets except that the effect of one electron cancels out the effect of its partner. Most electrons are paired and of opposite spin causing most material not to be magnetic.

Cont. In certain materials, cobalt, iron and nickel not all electrons are paired completely and thus not all magnetic fields cancel. These are called ferromagnetic materials. In such materials coupling occurs between neighboring atoms, forming large groups of atoms with spins that are aligned. (domains) When domains are randomly arranged the material is not magnetized. An external field can align domains resulting in magnetization.